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]]>Now the second part is that I moved to the US. I have learned that there are a lot of competitions held my top universities such as hmmt or pumac. I started to practice them. However, the official rule is that students are not allowed to use them. I have lost my best weapon in this competition but I have a strong desire to do well on them. Is there any advice that you could give to the students who are in similar situation as mine?

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]]>If I start at and jump down, why will I reach in a finite number of steps? has no immediate predecessor.

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]]>With these competitions, I first really got interested in math. Before, I didn’t even know what a proof is and would probably not have been as fascinated in math as I am now.

So indeed, math olympiads really were valuable!

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]]>To explain what I mean, if we set , we must have that , which means that is linear, at least for numbers of the form . Thus we must add the requirement that , no?

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